Bones Wont deform with Mesh
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It looks the automatic weighting failed when you tried to parent the mesh to the rig. This is unfortunately a common occurrence in Blender. It seems to happen when you use somewhat dense meshes like you have.

There is a really easy fix though. Select both the mesh and the rig and scale them up a lot. I tested your file and it worked when I scaled them up 100 times. All this does is space things out a bit (a lot) more and the automatic weighting seems to like that better. Then apply the scale on both objects with Ctrl+A. Then parent, scale down (by .01 instead of 100 this time) and apply the scale again.